Boundedness and Continuity of Fuzzy Linear Order-Homomorphisms on $I$-Topological\ Vector Spaces

In this paper, a new definition of bounded fuzzy linear order homomorphism on $I$-topological vector spaces is introduced. This definition differs from the definition of Fang [The continuity of fuzzy linear order-homomorphism. J. Fuzzy Math. {bf 5} textbf{(4)} (1997), 829–838]. We show that the ``boundedness «and `` boundedness on each layer» of fuzzy linear order homomorphisms do not imply each other. On the basis, characterizations of continuity of fuzzy linear order-homomorphisms, and the relation between continuity and boundedness are studied.